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SEMINAR:Combinational and geometric aspects of the group of projective..

Speaker:Michel Lavrauw, Sabancı University

Title:Combinational and geometric aspects of the group of projective motions of certain algebraic varieties

Date/Time:21 December 2022 / 13:40 - 14:30

Location: FENS G015 (Physical Only)

Abstract:In combinatorics and finite geometry, the study of algebraic groups and their various actions has often led to new constructions of interesting (rare) geometric objects. It is an essential feature of the interplay between groups and geometry. A well-known example, due to Jacques Tits from 1962, is the action of the Suzuki group on the points of a 3-dimensional projective space, giving rise to an ovoid (a notion introduced by Beniamino Segre): a set of points which has the same combinatorial and geometric properties as (but is not equivalent to) an elliptic quadric. Since then, this idea has matured, and the availability of computer algebra systems has greatly contributed to recent developments; there are many authors who have used so-called “orbit-stitching” to obtain new constructions of desirable (finite) geometries. In this talk we will focus on the action of the group of projective motions of certain algebraic varieties. The classification of their orbits on subspaces is a challenging task, and few classifications are complete. After a general introduction, I will explain some recent work, obtained jointly with Stefano Lia (University College Dublin) and Francesco Pavese (Politecnico di Bari), concerning the action of an algebraic group G ≤ PGL(4, q), isomorphic to PGL(2, q), arising from a maximal rational curve embedded on a smooth Hermitian surface with some fascinating properties. The study of its orbits leads to a new construction of a quasi-Hermitian surface: a set of points with the same combinatorial and geometric properties as a non-degenerate Hermitian surface.

Bio:Ayse Kivilcim Coskun is a full professor in the Electrical and Computer Engineering Department at Boston University and also serves as the Director of the Center for Information and Systems Engineering. Coskun received her Ph.D. degree from the Computer Science and Engineering Department at UC San Diego and her B.S degree in Microelectronics Engineering from Sabanci University. Coskun’s research interests are broadly in design automation, computer architecture, and embedded systems, particularly focusing on energy efficiency, thermal challenges, and using analytics for intelligent system management. Coskun received the IEEE CEDA Ernest Kuh Early Career Award in 2017 for contributions to energy-efficient system-level design and an IBM Faculty Award in 2020 for her work on applying AI-based methods to cloud software management. Coskun currently serves as the Deputy Editor-in-Chief of the IEEE Transactions on CAD and an Associate Editor for the ACM Transactions on Architecture and Code Optimization.